University of Groningen

Hot electron transport in metallic spin valve and graphene-silicon devices at the nanoscaleParui, Subir

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Chapter 2

Ballistic Electron Emission Microscopy andRelated Techniques

Abstract

Development of the Scanning tunneling microscope (STM) has led to the remarkableprogress in the field of surface characterization of conducting materials with atomic reso-lution. Beyond that, a modified version of this technique is used to hot electron transportand for microscopy studies in conducting thin films, known as Ballistic electron emis-sion microscopy (BEEM). In addition to that, visualization of spin transport was alsoachieved using the magnetic version of BEEM by locally mapping the spin-dependenttransport in spin valves. Although studies using hot electrons in solids were initiatedin the past, it is only in later years that numerous progress have been achieved, concern-ing the nanoscale measurement of hot electron transmission in various thin films. Inthis chapter, the main concepts of hot electron transport and BEEM are presented. Thechapter is based on published work in this field. We start with a brief introduction tothe working principle of BEEM followed by an overview of BEEM and other techniquesrelated to BEEM used in this research.

2.1 Introduction

Developed in the late 1980’s by Kaiser and Bell [1], Ballistic electron emissionmicroscopy (BEEM) is considered to be a versatile technique which can probe

both the energy and spatial dependence of transport of hot electrons in thin films. InBEEM, a Scanning tunneling microscope (STM) [2] is modified with an additionalelectrode to collect the hot electrons across a Schottky barrier. The main motiva-tion of this chapter is to give an overview of the ballistic hot electron transport insolid state devices and then to discuss briefly the nanoscale technique i.e., ballisticelectron emission microscopy (BEEM) and other related techniques derived fromBEEM. An overview of the BEEM theory is presented with a discussion of the twomost commonly used models namely, Bell-Kaiser (BK), and Ludeke-Prietsch (LP)model. The resolution of these techniques using few examples from published lit-erature are described. Here, we have discussed the parts of BEEM technique which

10 2. Ballistic Electron Emission Microscopy and Related Techniques

Metal Base Ballistic Hot Electron Transport

M/I/M/SS/M/S

High-Speed Unipolar Transistors

M = MetalI = InsulatorS = Semiconductor

M/I/M/I/M

Figure 2.1: A number of metal base unipolar hot-electron transistor devices. Out of these 3device structures, the M/I/M/S is similar to our BEEM related experiments.

are directly relevant to our own experimental work whereas a more detailed reviewabout BEEM can be found in Ref. [3, 4, 5]. This thesis includes results using BEEM,Ballistic hole emission microscopy (BHEM) [6, 7], Scattering (Reverse) BEEM andBHEM (RBEEM, RBHEM) [6, 8], and Ballistic electron/hole magnetic microscopy(BEMM/BHMM) [9, 10] which are presented in the later chapters.

2.2 Hot and Ballistic electrons

Hot electron phenomena have become important for the understanding of all mod-ern semiconductor devices. Electrons having energies higher than a few tenths ofone electron volt (eV) above the Fermi level of the system, are referred to as “hot”electrons. Electrons which contribute to the electrical conductivity in solids are freeelectrons with energies a few kBT (≈25 meV at 300 K) above or below the Fermilevel. If we make a simple analogy of the electron energy to the real lattice tem-perature (eV = kBT ) then electrons of energy 1 eV above the Fermi level wouldcorrespond to a temperature rise up to ≈12000 K [11]. However, those energies arenot accessible simply by increasing the temperature of the material. Here we thusconsider the kinetic energy (K.E.) of the hot electrons not the actual device tem-perature. In our research we focus on hot electron and hot hole transport throughmetallic multilayer, for energies in the range of 1 eV to 2 eV above (for electrons)and below (for holes) the Fermi level.

Above the Fermi energy, there are lots of unoccupied states for the hot electronsto occupy, in contrast to the thermal electrons where the energy levels are filled.Therefore the scattering mechanisms for hot electrons and electrons at Fermi level

2.2. Hot and Ballistic electrons 11

are very different. According to Fermi’s golden rule, the electron should find anempty states to scatter into, which is very unlikely for the electrons at the Fermilevel as all bands are filled as described by Fermi-Dirac distribution:

F (E) =1

1 + exp(E−EF

kBT

) (2.1)

So, to have scattering into the empty states, the maximum interaction energy of elec-tron is≈3kBT = 78 meV. Hence elastic or quasi-elastic scattering are the dominatingscattering processes at Fermi level, whereas inelastic electron-electron (e-e) scatter-ing becomes more dominant at these higher energies. The inelastic scattering of hotelectrons is caused by the Coulomb interaction with the other electrons below theFermi-level which excite the electron above the Fermi-level and this process is calledas Stoner excitation. Hot electrons loose a large part of their energy via this inelasticscattering event. Electron-phonon scattering is considered to be a quasi-elastic pro-cess, since hot electrons can suffer only an energy loss of the order of kBT , whichis not significant compared to the initial electron energy. Defects and impurity scat-tering of electrons are always present in any metal and introduce a temperatureand energy independent elastic scattering contribution [12]. However, if during thepropagation through the metal base, the hot electrons stay unscattered between twoscattering events, they are called “ballistic” electrons. In ideal situation ballistic hotelectrons do not lose energy or undergo a change in momentum and form the majorcontribution to the collector current. Metal base ballistic hot electron transport canbe realized in three different device structures as shown in the Fig. 2.1 and they arediscussed in the next subsection.

2.2.1 Hot electron devices

Successful commercial utilization of hot-electron phenomena is a Gunn diode, basedon the intervalley transfer mechanism for a negative differential resistance. A hotelectron device using three electrodes in a triode configuration was first demon-strated by Mead in the year of 1961 [13]. Recently, semiconductor devices based onhot electron effects have made remarkable progress in the field of spintronics. Ingeneral a three-terminal transistor-like device can be fabricated for ballistic hot elec-tron creation and detection in an all-solid-state structure as shown in Fig. 2.2a, b,and c. In these three terminal devices, hot electrons are injected by an emitter elec-trode through a Schottky or a tunnel barrier into a thin metallic base electrode. Thebase electrode is separated from the subsequent collector electrode by a similar po-tential barrier which acts as an energy filter. If the electron injection energy is higherthan the base/collector barrier height and the base is thin enough so that a fraction

12 2. Ballistic Electron Emission Microscopy and Related Techniques

M IM MI

c)

BaseContact

Graphene (Base)

+

BCI (Al O )2 3

EBI (SiO )2

g)

M SMI

b)

f )

S SM

a)

e)

Figure 2.2: The top panel shows the energy-band diagrams of metal-base transistors: a)S/M/S, b) M/I/M/S and c) M/I/M/I/M respectively under operating bias conditions. Thebottom panel is for the respective examples of real devices as reported in literatures. Figuresd), e) and f) are taken from Ref. [14], [15], and [16] respectively.

of the injected electrons can cross it ballistically, then those hot electrons are eligibleto overcome the collector barrier and contribute to the collector current. Three ofsuch device concepts are used: i) in spin valve transistor as in Fig. 2.2d, ii) for theinvestigation of spintransport in Si in Fig. 2.2e and iii) for the graphene-based hotelectron transistor in Fig. 2.2f.

The concept of BEEM experiment is very similar to the M/I/M/S device con-figuration as shown in Fig. 2.2b. The most essential part of the BEEM device is therectifying metal/semiconductor Schottky interface which is used as the energy fil-ter of the hot charge carriers. In the next section, we thus discuss the basic theory ofsuch rectifying M/S interface whereas the detailed understanding can be found inthe text books [17, 18].

2.2.2 Rectifying metal/semiconductor (M/S) Schottky collector

When a M/S interface is formed there will be a flow of free carriers from one ma-terial to the other due to the mismatch in Fermi levels and a potential barrier willbe established between the metal and semiconductor called as Schottky barrier. Fora n-type semiconductor when a metal layer is deposited to make electrical contact

2.2. Hot and Ballistic electrons 13

E g

E F

фm

χ

фB(n)

Wd

Vacuum Level

Metal n-Semiconductor

E g

E F

фm

χ

фB(p)

Vacuum Level

Metal p-Semiconductor

a) b)

Figure 2.3: Representation of the Schottky barriers between metal with n-type (a) or p-type(b) semiconductors.

then there will be a flow of electrons from the n-type semiconductor to the metal.Since there is a net flow of charge carriers there will be an accumulation of electronsat the metal side and a space charge will build up between the two surfaces. Thisaccumulation will grow until there is no more net charge carrier flow and a thermalequilibrium is established resulting in the lining up of both Fermi levels. Due to thespace charge there will be an internal electric field across the M/S interface whichwill result in a potential difference between the metal and the semiconductor bulkcalled the contact potential. The carrier density in the metal is much higher than inthe semiconductor, therefore the space charge region is much deeper in the dopedsemiconductor than in the metal. The width of the space charge layer in the semi-conductor which is completely depleted of electrons is denoted by Wd. When themetal and semiconductor are in contact an equilibrium will be established as shownin Fig. 2.3a. The barrier height between the metal and the semiconductor withoutconsidering any interface states is then given as:

φB(n) = φm − χ (2.2)

where φm is metal work function, χ is electron affinity of the semiconductor andthus φB(n) is completely determined by bulk material properties. This relation iscalled the Schottky-Mott relation. Similarly for a p-type semiconductor as shown inFig. 2.3b, the barrier height will be:

φB(p) = Eg − (φm − χ) (2.3)

where Eg is the band gap of the semiconductor.

14 2. Ballistic Electron Emission Microscopy and Related Techniques

Thermionic emission theory

The electrical transport across the Schottky barrier is described by thermionic emis-sion theory [17, 18]. It is assumed that the flux of electrons emitting from the surfaceis equal to the flux of electrons received on the surface. The flux of electrons arrivingat the surface is defined as the number of electrons passing through a unit area perunit time and is given by:

J = enν (2.4)

where e is the electrical charge of an electron, n is the electron concentration whichis determined by Maxwell-Boltzmann statistics and ν is the mean velocity of theelectrons. Using this and subtracting the current which flows from the metal to thesemiconductor JM→S from the current flowing from the semiconductor to the metalJS→M the following expression for the total current density Jn can be given:

Jn = JS

[exp

(eV

kBT

)− 1

], where JS = A∗T 2exp

(− eφBkBT

)(2.5)

where JS is the saturation current density and A∗ is the Richardson constant forthermionic emission of electrons from the semiconductor to the metal, V the voltageapplied to the Schottky barrier and T the temperature. A∗, which takes into accountthe effective mass, is defined as:

A∗ =4πem∗ek

2B

h3. (2.6)

Apart from the Richardson constant there are other effects which play a role inthermionic emission. These are the quantum mechanical transmission effect andelectric-field-enhanced emission. The Richardson constant can be modified to ac-count for these effects and is called the effective Richardson constant A∗∗. Exam-ples of the effective Richardsons constant are: A∗∗ ≈ 110 and 30 A·cm−2·K−2 forn-Si and p-Si respectively. The final equation describing the charge transport whenthermionic emission is dominant becomes:

J = JS

[exp

(eV

ηkBT

)− 1

]≈ JS

[exp

(eV

ηkBT

)]for eV ≥ 3kBT. (2.7)

Where JS now uses the effective Richardson constantA∗∗ and η is the ideality factordescribing the deviation from the ideal situation. For η = 1, the current transportprocess is pure thermionic emission. However, thermionic emission is not the onlyprocess which scales exponentially with the applied voltage and then the diode canbe non ideal with η > 1.

The Schottky barrier height, φB can also be directly measured as an onset of theBEEM current and it should be comparable with the value obtained from such I-Vmeasurement with η ≈ 1.

2.3. Ballistic Electron Emission Microscopy (BEEM) 15

n-type Semiconductor

Metal

e-

IT

VT-+

IB

STM tip

Figure 2.4: The BEEM setup is visualized with the electrical circuit attached to it. A constanttunnel current IT is injected at variable tunnel voltages VT . The injection and acceptancecones are visualized by the orange cones (∅ ≈ 1 nm). Electrons which surpass the SB aredetected as BEEM current IB .

2.3 Ballistic Electron Emission Microscopy (BEEM)

BEEM is a modified form of a scanning tunneling microscope (STM) allowing thenanoscale study of nonequilibrium carrier transport across buried interfaces. Thedifference from a normal STM setup is the addition of a back contact to the sample.This makes it possible to collect the injected electrons which have traveled throughthe complete device. The basic schematics of this is shown in Fig. 2.4. The current isinjected perpendicular to the layer stack in a current-perpendicular-to-plane (CPP)geometry. The transport of the hot electrons can be divided in four different stages:

1. Injection of the charge carriers from the tip into the metal base,

2. Transport through the metal base,

3. Transmission across the M/S interface,

4. Transport through the semiconductor.

Charge carriers are injected from the tip by tunneling into unoccupied statesof the thin metal base. This results in an angular and energy distribution of theinjected carriers at the metal surface. After the injection, the hot charge carriers willpropagate through the metal film. When the carriers reach the interface and satisfythe energy and momentum criteria at the interface, they can be transmitted throughthe M/S interface and enter the semiconductor. Finally, after transport across thesemiconductor the electrons will be collected and form the BEEM current. Due to

16 2. Ballistic Electron Emission Microscopy and Related Techniques

EF(T)

e-

a)

EF(M/S)

MetalTip n-type SC

VT φB

V0

VT

IB

b)

Hot e-

0

0

Figure 2.5: a) A schematic energy level diagram of a negatively biased tip with the hot elec-tron distribution in red. Note that not all the electrons from this distribution have sufficientenergy to pass the barrier. b) Typical BEEM spectrum, with the threshold value V0, whichcorresponds to the Schottky-barrier height φB = eV0.

the very local nature of injecting electrons and the requirement of lateral momentumconservation at the interface this technique results in a very high spatial resolutionimaging.

2.3.1 Spectroscopy and imaging

The most widely used mode of the BEEM technique is the spectroscopy mode whichprovides information on local transport characteristics of hot electron between theSTM tip and the semiconductor. The simplified energy band diagram of the BEEMexperiment is shown in Fig. 2.5 together with the BEEM current with respect tothe sample tip bias. The BEEM current consists of a small fraction of the injectedelectrons which satisfy the necessary energy and momentum criteria for collectionacross the M/S interface. No BEEM current will be observed when the tip bias isbelow the Schottky barrier height. By gradually increasing the tip bias, the BEEMcurrent can be observed beyond a certain onset which corresponds to the Schottkybarrier height. The higher the tip bias, more electron will contribute to the BEEMcurrent. A BEEM spectra thus can be obtained by recording the BEEM current withrespect to the tip bias at a fixed tip position. In general to improve the signal tonoise ratio several BEEM spectra are recorded to obtain a single averaged spectrum.The final BEEM spectrum provides the information of energy dependence of hotelectron transport in the metal film as well as the M/S interface. The onset of theBEEM spectra determines the Schottky barrier height with high accuracy (≈ 0.01eV) whereas the spectral shape carries information about scattering in the metalfilm, across the M/S interface and in the semiconductor.

2.3. Ballistic Electron Emission Microscopy (BEEM) 17

Figure 2.6: (a) STM topography and (b) simultaneously recorded forwarded BEEM currentimage at 77 K on epitaxial CoSi2/n-Si(100) surface (VT =1.5 V, IB=3 nA, film thickness =3.8nm). Two different surface reconstructions are apparent, and the BEEM contrast reflects theatomic scale periodicity of the surface topography. The BEEM contrast ranges from 25 pA(black) to 55 pA (white). Adapted from Ref. [20].

A direct spatial map of the BEEM transmission can be obtained by using theBEEM imaging mode. Using the capability of the STM tip to scan the conductingsurface, the BEEM image can be mapped by simultaneous recording the BEEM cur-rent at a fixed tip bias above the threshold value. A comparison between the BEEMimage and the surface image provides information about the transport characteris-tics with respect to the structural properties of the metal film and the M/S interface.Although it is not always very easy to interpret the lateral variation of the BEEMimage, the possible reasons for inhomogeneous interface transmission are due tolocal variation in the metal layer thickness, variation in the local Schottky barrierheights, lateral variation in the interface bonding across the M/S interface etc. Suchvariation in BEEM current can be at a length scale of few A as discussed latter.

Resolution of BEEM

Using the spatial variation of BEEM current it is possible to determine the resolutionof the technique. An important feature of BEEM is that the resolution of BEEMimaging is not limited by the technique but by the structure of the sample beingimaged. Lateral resolution of BEEM has been established by Miliken et al., [19] on apolycrystalline Au/Si(111) sample with SiO2 patterns on top. From the sharp onsetof the BEEM current in the absence of SiO2, it has been shown that the resolutionof BEEM is 10 A. Even further, much better resolution has been demonstrated bySirringhaus et al., [20] in an epitaxial system of CoSi2/Si(100). Figure 2.6(a) showsatomically resolved CoSi2 surface topography whereas Fig. 2.6(b) corresponds to theBEEM current variation also with atomic periodicity. In presence of surface point

18 2. Ballistic Electron Emission Microscopy and Related Techniques

defects like missing adatom as indicated by the arrow in the surface topography,local BEEM current increases which confirms BEEM has an atomic scale resolution.

2.4 BEEM Theory

In order to extract the Schottky barrier height from spectroscopy measurements atheoretical model is needed to fit the data. The first theoretical description dealingwith the transport of hot-charge carriers through a metal-semiconductor system ina BEEM setup was proposed by Bell and Kaiser. As mentioned before, the transportof the charge carriers can be characterized into four different regions. The processesdescribed in this chapter are for hot electrons due to the use of n-type silicon sub-strates and the theory is also valid simultaneously for hot holes.

2.4.1 Tunnel injection of non-equilibrium charge carriers

The applied potential between the tip and the metal base, called the tip voltageVT , will determine the energy of the injected electrons. Tunneling across the poten-tial barrier between the tip and the metal will always result in a distribution of theenergy and momentum of the electrons. In common BEEM theory [1] the tunnel in-jection of non-equilibrium electrons from the tip into the base is assumed to behaveaccording to the planar tunneling theory [21]. Although it has been shown that it isnot always valid to use planar tunneling theory, the voltage spectroscopy measure-ments with BEEM are found to agree well with planar tunneling based theory [22].At tip voltages close to the threshold results in a sharply peaked distribution of theinjected electrons perpendicular to the M/S interface. Therefore the injected elec-trons will have little momentum parallel to the metal base (k‖ � k⊥).

2.4.2 Transport across the metal base

Due to scattering, the spatial and energetic distribution of the electrons will broadenwhen traversing the metal base. The hot electron attenuation length can be de-scribed by a single parameter called the attenuation length λ(E) which in principleis energy dependent. The attenuation can than be described by an exponentially de-caying function depending on the injection angle θ away from the surface and metalfilm thickness d:

IB(t, E)

IT∝ exp

[−d · cos(θ)

λ(E)

](2.8)

Since the electrons are injected with almost zero parallel momentum k‖ = 0 we canassume cos(θ) ≈ 1 simplifying the equation.

2.4. BEEM Theory 19

EF(T)

EF(M/S)

MetalTip n-type SC

1

2

33

3 4

4

Figure 2.7: Four different scattering mechanisms in a forward biased BEEM experiment,where a • denotes electrons and a ◦ denotes holes. (1) pure ballistic transport (green), (2)inelastic scattering in the metal film (blue) which can lead to secondary electrons (also blue),(3) elastic scattering in the metal film or the interface (purple) and (4) impact ionization, wherea electron hole pair is created (red).

2.4.3 Scattering mechanisms

All of the different scattering processes which are relevant for our studies in thisthesis occur in the metal base. In Fig. 2.7 the most prominent scattering mechanismsare depicted, which are:

Ballistic transport Ballistic transport is the unscattered propagation of electronsthrough the metal base. If the electrons travel ballistically through the metal basethey might have enough energy, depending on VT , to surmount the Schottky barrierat the M/S interface.

Inelastic scattering If the electrons are scattered inelastically their energy will bereduced. The processes dominating this form of scattering, at the energies is electron-electron (e-e) scattering [6] and will typically result in a reduction of half the elec-tron energy. At low tip voltage this effectively means that any inelastically scatteredelectron will not have enough energy to surmount the Schottky barrier. Howeverat higher tip voltages, at least at an energy twice that of the Schottky barrier, thecollision might result in a secondary electron with enough energy to surmount theSchottky barrier along with the primary electron that still has an energy above theSchottky barrier, thereby increasing the BEEM current. Although phonon scattering

20 2. Ballistic Electron Emission Microscopy and Related Techniques

can also result in energy loss they are not taken into account since the change inenergy is negligible small, on the order of kBT , in comparison with e-e scattering.

Elastic scattering This form of scattering will change the momentum but conservethe total kinetic energy of the electrons. Therefore any elastic scattering will result ina broadening of the distribution of angular momentum. Since transmission acrossthe M/S interface is sensitive on the momentum, as shown in section 2.4.5, elasticscattering will also have an effect on the BEEM current. Grain boundaries, impuri-ties, defects and any inhomogeneities in general are the main elastic scattering sites.

Impact ionization When an electron with high enough energy enters the semi-conductor it could transfer a part of its energy to an electron in the valence band. Ifenough energy is transfered it could excite the electron to the valence band creatingan electron-hole pair. This electron could then contribute to the BEEM current. Forthis however the impacting electron should have an excess energy above the thresh-old of more than twice of the semiconductor band gap. Since all experiments areperformed below this limit, impact ionization is not present.

2.4.4 Electron attenuation length

With increasing metal base thickness the BEEM current is attenuated. The total at-tenuation length, λ is related to the inelastic attenuation length, λi and the elasticattenuation length, λe as described by Matthiessen’s rule:

1

λ(E)=

1

λe+

1

λi(E)(2.9)

From equation 2.8 it is clear that the transmission exponentially depends on the filmthickness of the metal base. Therefore, by varying the metal base layer thicknessand measuring the transmission at a particular energy a plot can be obtained of thetransmission versus metal base thickness and energy. Using an exponential axisfor the transmission, the slope of the plot gives the electron attenuation length ata particular energy. The energy dependence of the attenuation length can now beobtained by repeating this process at different energies. By BEEM λe and λi(E) cannot be measured directly. However, the inelastic attenuation length is energy depen-dent and proportional to the product of the group velocity and the inelastic electronlifetime. Using Fermi liquid theory the energy dependent inelastic scattering can bedescribed as: λi(E)∝ (E+EF )0.5/E2,EF is the Fermi energy of the metal. Althoughthere are possibilities to extract the two different attenuation lengths λi and λe fromλ but this is generally not so straight forward.

2.4. BEEM Theory 21

2.4.5 Transmission across the M/S interface

The transmission across the barrier is dependent on the energy and the momentumof the incoming electron. Assuming the electrons satisfy the 2D free electron model,their energy would be given as:

E =~2

2m(k2⊥ + k2‖) = E⊥ + E‖ (2.10)

Where m is the rest mass of the electron (free electron mass) and k⊥ and k‖ are themomentum of the electron perpendicular and parallel to the M/S interface, respec-tively. The energy of the electron just at the maximum of the Schottky barrier heightcan now be expressed as:

E =~2

2m∗(k2⊥S + k2‖S) + EF − eV + φB (2.11)

Where m∗ is the effective mass of the electron inside the semiconductor, EF is thetip Fermi energy, φB is barrier height at the M/S interface and the subscript of kSdenotes the momentum in the semiconductor. If we consider the conservation oftransverse momentum (which is parallel to the interface k‖) for the electron to enterfrom metal to the semiconductor, we can obtain an analytical expression for the ‘re-fraction’ for maximum allowed transverse momentum. Specifically, conservation oftransverse momentum defines a critical angle for electron propagation in the metalbase outside of which electrons may not be collected in the semiconductor, similarto the acceptance cone at the M/S interface and is defined as [1]:

sin2θc =mt

m

eV − φBEF + eV

(2.12)

where mt is the transverse electron effective mass in the semiconductor (mt = 0.19min Si). This argument would only be convincing for a perfectly epitaxial systemwithout any defects, any deviations of such a system would break the symmetryand therefore conservation of transverse momentum could be relaxed to a certaindegree.

2.4.6 BEEM transport models

The tunnel current between tip and top metal based on planar tunneling theory canbe written as:

IT = A

∞∫0

dE⊥T (E⊥)

∞∫0

dE‖[f(E)− f(E + eVT )] (2.13)

22 2. Ballistic Electron Emission Microscopy and Related Techniques

T (E⊥) is the tunnel probability for an electron to tunnel through the vacuum barrierover the transverse and parallel (to the interface) energies, E⊥ and E‖. A is theconstant related to effective tunneling area, f(E) is the Fermi distribution function,and VT is the applied tip voltage.

According to widely used Bell-Kaiser (BK) model[1], BEEM transmission is thefraction of the ballistically transmitted tunnel current:

IB = AR

∞∫Emin

⊥

dE⊥T (E⊥)

Emax‖∫0

dE‖[f(E)− f(E + eVT )] (2.14)

Where R is an attenuation factor due to scattering in the metal base and the M/Sinterface. According to BK model, R is considered to be energy independent butit can also be weakly dependent on energy. Other parameters, Emin⊥ =EF -e(VT -φB)and Emax‖ =[mt/(m-mt)]×[E⊥-EF+e(VT -φB)].

For VT just above φB , close to threshold, above equations (2.13), (2.14) predict:

IB∝IT (VT − φB)2 (2.15)

Such quadratic onset considers classical transmission across the M/S interface withparabolic conduction band minimum in the semiconductor. Considering quan-tum mechanical transmission across the M/S interface another model was givenby Ludeke-Prietsch (LP model) according to which IB∝IT (VT − φB)2.5 [3]. It wasfound that near the threshold regime, no significant difference between the BK andLP models can be resolved beyond experimental error. Increasing the bias voltageapproximately 0.2 - 0.3 V above the threshold the BEEM current starts varying lin-early with the tip bias showing that the theory only models the BEEM current veryclose to threshold. For the Schottky barrier extraction in our experimental measure-ment we have considered BK model instead of LP model and we have seen a bettermatch with the macroscopic I − V measurements.

2.5 Techniques related to BEEM

In a standard BEEM experiment, an n-type semiconductor substrate is used as thecollector and a negative tip bias is applied to inject electrons into the base. A frac-tion of the injected hot electrons can then be collected as collector current. Usinga positive tip bias, holes can be injected into the base and in order to collect theseholes directly one needs to use a p-type semiconductor. So the devices can be fab-ricated by using either an n-type or a p-type semiconductor. However the use of ap-type semiconductor is not the only way to record BEEM current with a positive

2.5. Techniques related to BEEM 23

EF(M/S)

Tip n-type SC

Hot e-

Metal

h+VT

EF(T)

Excited e-

h+

1

2

Vacuum barrier

EF(M/S)

Tip p-type SC

Hot h+

Metal

VT

EF(T)

Vacuum barrier

h+ φB‘

a) b)

Figure 2.8: (a) Energy diagram of a BHEM experiment. Hot holes are injected into the metalbase grown on top of a p-type semiconductor and a fraction of them are being collected inthe valence band of the semiconductor. (b) Energy diagram of reverse BEEM experimentwhich enables scattering spectroscopy. Hot holes are injected into the metal base on a n-typesemiconductor collector. Inelastic scattering in the metal base creates electron-hole (e-h) pairswhich cause collection of hot electrons in the conduction band of the semiconductor.

tip bias. In the case of n-type substrates, injected holes can scatter and form a distri-bution of hot electrons that can then be collected. In this section we have discussedall these possibilities as the “Ballistic Hole Emission microscopy (BHEM)” when thesubstrate is p-type with hole injection and the “Scattering (Reverse) BEEM” whenthe substrate is n-type but with hole injection as shown in Fig. 2.8.

2.5.1 Ballistic Hole Emission Microscopy (BHEM)

The technique of hot electron study in BEEM can equally be well applied for non-equilibrium holes, in a device structure consisting with a p-type collector. Thetechnique is then often referred as ballistic hole emission microscopy (BHEM). Theworking principle of the technique is as follows: The STM tip is positively biasedwhich injects electrons into the tip, and therefore holes into the base through vac-uum tunnel barrier. A fraction of the injected holes that satisfy the energy and mo-mentum criteria are then collected in the valence band of the semiconductor. Ballis-tic electrons in BEEM are used to probe conduction band structure whereas ballisticholes in BHEM are used as a probe of the valence band structure of the same semi-conductor. BHEM was demonstrated by Bell and serves as a direct measurementof the p-type Schottky barrier height. The behavior of a typical BHEM spectrumclose to threshold is similar to the BEEM spectrum. The collected current has aIC(Hole) ∝ IT (V − φB)2 dependence, where φB is the Schottky barrier height witha p-type semiconductor. Although BEEM and BHEM are very similar but the dis-tribution of hot holes is exactly opposite to the distribution of hot electrons. The

24 2. Ballistic Electron Emission Microscopy and Related Techniques

tunneling electron distribution is peaked at the Fermi level of the negative electrodewhich is the STM tip in the case of hot electrons and metal base in the case of hotholes and such asymmetry in the distribution causes a difference in hot hole and hotelectron scattering at higher biases.

2.5.2 Scattering (Reverse) BEEM

The direct electron and direct hole spectroscopies can be used to probe conductionand valence band structure of the M/S interface with n and p-types semiconductorrespectively. These mode of operation are considered to be the forward bias ex-periment where majority carriers are injected and a fraction of them are collected.However, there is another way to study the scattered carriers by probing only thosecarriers which are created in the process of scattering and is referred to scattering(Reverse) bias BEEM experiment. In the case of n-type semiconductor collector,electrons will be extracted from the metal film creating a ballistic hole distributionin which the technique relies on the detection of only secondary electrons created inthe process of carrier-carrier scattering. Such process is very similar to the “Augerlike” scattering process.

In the case of R-BEEM process[8], hot holes are injected (electrons are extracted)by the tip to the base and they are filled by electron-hole collisions. Energy of theinjected holes transfered to the excited electrons can be maximum up to the kineticenergy ofEF,b+eVT . If the secondary electrons have enough energy and momentumto surmount the barrier, they can be collected as collector current with the same signas direct BEEM. Considering free electrons and zero temperature, R-BEEM transmis-sion can be written as:

IRB = AR

EF,b∫EF,b−eVT

dE

E∫0

dE⊥P (E,E⊥)T (E⊥) (2.16)

where EF,b is the base Fermi energy, P (E,E⊥) is the probability of creation of ex-cited electrons from the injected hot holes. The excited electrons are then collectedabove φB with proper momentum. Near threshold, the above expression of R-BEEMtransmission can be simplified as:

IRB∝IT (VT − φB)4. (2.17)

Considering the quantum mechanical transmission of electrons at the M/S interface,the power of the above equation will be 4.5 (LP model) instead of 4 (BK model) andsimilarly an analogous R-BHEM experiment can also be performed using a p-typesemiconductor.

2.6. Ballistic Electron and Hole Magnetic Microscopy(BEMM and BHMM) 25

Direct and reverse BEEM involve electron and hole injection from the tip to thebase respectively. It is also important to consider the distribution of injected carriersfor scattering in the base. When electrons are injected into the base, the distributionof electrons are maximum at the applied bias to tunnel through. But hole injection iscompletely opposite. The hot hole distribution is maximum close to the Fermi levelof the base so less number of hot holes tunnel through the barrier. Such differencein distribution plays important role for hot electron and hot hole scattering whichreflects also in the BEEM and R-BEEM spectral shape.

In case of R-BEEM, collected transmission is also expected to be decreasing withincreasing thickness but differently than direct BEEM. Similar exponential decay canbe obtained as:

IRB(t, E)

IT∝ exp

[− t

λeff (E)

](2.18)

λeff (E) is the effective attenuation length governs by the diffusion length for inelas-tic collisions. Such characteristic length is the cumulative effect of hole attenuation,creation efficiency of excited electron and then the decay of isotropically distributedexcited electron.

2.6 Ballistic Electron and Hole Magnetic Microscopy(BEMM and BHMM)

Ballistic electron magnetic microscopy (BEMM) was first introduced as the magneticcounterpart of BEEM by Rippard and Buhrman in 1999 [9]. The technique is basedon the spin-dependent hot electrons scattering in ferromagnetic thin films, in whichthe minority spin electrons are attenuated more strongly than the majority spin elec-trons. This is very similar to that of the classical “polarizer-analyzer” experiments ofoptics where the angle between polarizer and analyzer controls the output intensityof the transmitted beam. Similarly, the BEMM current above the Schottky barrieris high when the magnetizations of both ferromagnetic layers of the spin-valve arealigned parallel (P) and low when they are aligned anti-parallel (AP) controlled byan external applied magnetic filed.

The concept of BEMM experiment is very similar to that of the magnetic tunneltransistor (MTT) where the injection of hot electrons is by the STM tip through anideal vacuum tunnel barrier as shown in Fig. 2.9 instead of a physical barrier. Thereare two magnetic layers (FM I and FM II) present which are necessary to fabricatethe magnetic sensor. The lower normal metal is used for good growth on the n-type semiconductor with a well-defined and homogeneous Schottky barrier at theM/S interface. The middle normal metal is used as a spacer layer. This means that

26 2. Ballistic Electron Emission Microscopy and Related Techniques

Semiconductor (n-type)

Transmitted electrons

IT

VT

IB

STM Tip

x y

z

Mag. �eld

Spin valve

FM I NM FM II NM

Figure 2.9: Schematic of ballistic electron magnetic microscopy. The tip of a scanning tun-neling microscope (STM) is used to inject hot electrons into a ferromagnetic thin film stackconsisting of two ferromagnetic thin films (FM I, FM II), separated by a thin non-magneticlayer (NM). The current in the semiconductor collector depends on the relative orientation ofthe magnetization of the two magnetic layers.

it separates the two magnetic layers, so that they will not interact directly. For anex-situ transfer of the device from the deposition system to the measurement setup, a capping layer is grown, to prevent oxidation of the top magnetic layer. Theinjected unpolarized hot electrons by the STM tip become strongly spin polarizedas they pass through the ferromagnetic thin films due to spin dependent scatteringin the ferromagnetic layers. The collector current strongly depends on the localmagnetizations of both ferromagnetic layers. The spin dependent collector current,IB , for the P and AP configuration, can be written as [26],

IPB ∝ (TMFM1TSTMFM2 + TmFM1TST

mFM2) (2.19)

IAPB ∝ (TMFM1TSTmFM2 + TmFM1TST

MFM2) (2.20)

where TM and Tm refer to the transmission of the majority (M) and minority (m) hotelectrons in the ferromagnetic layers, and TS is the transmission in the spacer (non-magnetic; NM) layer. When the magnetizations of the two ferromagnetic layers areparallel (P), then only one of the spin-channels (spin minority) will be strongly scat-tered and the other channel (spin majority) will be less scattered during transport

2.6. Ballistic Electron and Hole Magnetic Microscopy(BEMM and BHMM) 27

through the spin valve structure. But when the ferromagnetic layers are in anti-parallel alignment, both of the spin-channels will be strongly scattered when pass-ing through the spin valve structure. As a result the collected BEMM current will bemaximum for P-orientation and minimum for AP-orientation. Similar experimentcan also be done with the hot holes in a spin valve on a p-type semiconductor andthe technique is then called as Ballistic hole magnetic microscopy (BHMM).

Magnetocurrent (MC)

As discussed previously, the signal in the P condition will be higher than in the APcondition and a measure of this difference is called as the magnetocurrent (MC). TheMC is defined as:

MC =(IP − IAP )

IAP× 100% (2.21)

Thus the MC is very sensitive to the IAP and relatively less sensitive to the IP . TheMC can never be below -100%, but it has no upper limit. In an epitaxial spin valve,the MC increases with a high quality interface and a good decoupling between theferromagnets. Thus in general a higher MC corresponds to the highly efficient spintransport in the spin valve.

2.6.1 Resolution of magnetic imaging

By scanning the STM tip over such a spin valve device, a magnetic image of thetransmitted electrons can be obtained simultaneously with the surface topography.The contrast of the image gives information about the relative magnetization ori-entation of ferromagnetic films. An example of such magnetic images is shown inthe Figure 2.10. The measurements have been performed by BHMM on a spin valvestructures deposited on a p-type semiconductor [25] and Figs. 2.10a and 2.10b showthe magnetic images taken on a Co/Au /NiFe spin valve [10] in AP and P condi-tions respectively. The lighter (darker) areas in the image correspond to the ferro-magnetic films being in P (AP) magnetic orientation. For an applied magnetic fieldof -30 Oe, most of the regions are in AP state with minimum hole current of about0.55 pA. However, there is a region with narrow ring-like structure with larger holecurrent which is attributed to the 360◦ domain wall. For -100 Oe applied field bothmagnetic layers are saturated and the signal is almost homogeneously bright withlarger parallel current. Taking a line cross section across a 360◦ domain wall, themagnetic resolution can be determined as shown in the Fig. 2.10c. The line profileis described by a simple arctan function (solid line) for one side of the wall and theupper limit of the magnetic resolution is determined to be 28 nm. In this thesis in

28 2. Ballistic Electron Emission Microscopy and Related Techniques

a) b)

c)

Figure 2.10: BHMM images taken on a Co/Au/NiFe spin valve in subsequent magnetic fieldsof (a) - 30 Oe (AP) and (b) -100 Oe (P) at VT = -1.6 V, IT = 3 nA, T= 150 K of scanning area2×2 µm2. Hole current ranges from 0.5 pA (black) to 1.1 pA (yellow). In (c), a cross section isshown taken along the white line marked in (b). Taken from Ref [10].

chapter 6, we have demonstrated magnetic resolution using hot electron current inBEMM experiment which is below 20 nm.

2.7 Summary

In summary, the concept of hot electron and its ballistic transport in a metal basedsolid state device (macroscopic) with few important examples from the literatureare discussed. Then, the basic working principle of the microscopic or local tech-nique i.e. ballistic electron emission microscopy and how it has been extended forthe imaging of magnetic domains in a spin valve device structure are described. Dif-ferent modes of the technique which can be used for direct hot electron, direct hothole and scattered hot carriers transport through the over-layer and locally probethe metal-semiconductor interface are also highlighted. An introduction to BEEMtheory has been described using Bell-Kaiser model which has been used for the lo-cal Schottky barrier extraction. The experimental demonstration of the resolution ofBEEM and BHMM have been presented with few earlier examples from the litera-ture and issues regarding resolutions are also discussed.

2.7. Bibliography 29

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